%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:17:29 PM UTC 2026
% Result : Theorem 106.39s 14.14s
% Output : Proof 106.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 25
% Syntax : Number of formulae : 192 ( 138 unt; 0 def)
% Number of atoms : 298 ( 107 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 218 ( 112 ~; 73 |; 19 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 225 ( 6 sgn 123 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t44,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_lines(X2,X3),apart_point_and_line(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t97,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_lines(X2,X3),apart_point_and_line(X1,X3)),true) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t188,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t16]) ).
fof(f31,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f31_nnf,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c38,plain,
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t35,plain,
or(not(equal_lines(X1,X2)),not(distinct_lines(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t144,plain,
or(not(equal_lines(X1,X2)),not(distinct_lines(X1,X2))) = true,
inference(orient,[status(thm)],[t35]) ).
fof(f35,conjecture,
! [X,Y,Z] :
( ( equal_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( equal_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,Z] :
( ( ~ equal_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& equal_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( ~ equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))
| ~ convergent_lines(sk0,sk2) )
& equal_lines(sk1,sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c47,plain,
equal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t6,plain,
equal_lines(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t185,plain,
equal_lines(sk1,sk2) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t186,plain,
true = or(not(true),not(distinct_lines(sk1,sk2))),
inference(cp,[status(thm)],[t144,t185]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t313,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t14431,plain,
true = or(false,not(distinct_lines(sk1,sk2))),
inference(step,[status(thm)],[t186,t313]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t79,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t14432,plain,
true = not(distinct_lines(sk1,sk2)),
inference(step,[status(thm)],[t14431,t79]) ).
cnf(t582,plain,
not(distinct_lines(sk1,sk2)) = true,
inference(orient,[status(thm)],[t14432]) ).
cnf(t583,plain,
false = ifeq(true,true,distinct_lines(sk1,sk2),false),
inference(cp,[status(thm)],[t188,t582]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t77,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t14433,plain,
false = distinct_lines(sk1,sk2),
inference(step,[status(thm)],[t583,t77]) ).
cnf(t584,plain,
distinct_lines(sk1,sk2) = false,
inference(orient,[status(thm)],[t14433]) ).
cnf(t590,plain,
true = ifeq(apart_point_and_line(X1,sk1),true,or(false,apart_point_and_line(X1,sk2)),true),
inference(cp,[status(thm)],[t97,t584]) ).
cnf(t14628,plain,
true = ifeq(apart_point_and_line(X1,sk1),true,apart_point_and_line(X1,sk2),true),
inference(step,[status(thm)],[t590,t79]) ).
cnf(t1371,plain,
ifeq(apart_point_and_line(X1,sk1),true,apart_point_and_line(X1,sk2),true) = true,
inference(orient,[status(thm)],[t14628]) ).
fof(f10,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t76,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t108,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(orient,[status(thm)],[t76]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi6,axiom,
ifeq(convergent_lines(X0,X1),true,or(distinct_lines(X1,X2),convergent_lines(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c46,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi30,negated_conjecture,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t23,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi30]) ).
cnf(t148,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t189,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t191,plain,
true = or(distinct_lines(sk1,sk0),false),
inference(cp,[status(thm)],[t148,t189]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t78,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t14379,plain,
true = distinct_lines(sk1,sk0),
inference(step,[status(thm)],[t191,t78]) ).
cnf(t342,plain,
distinct_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t14379]) ).
cnf(t353,plain,
true = ifeq(distinct_points(X1,X2),true,ifeq(true,true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),true),
inference(cp,[status(thm)],[t108,t342]) ).
cnf(t16434,plain,
true = ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),
inference(step,[status(thm)],[t353,t77]) ).
cnf(t13251,plain,
ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true) = true,
inference(orient,[status(thm)],[t16434]) ).
fof(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f30_nnf,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c37,plain,
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t25,plain,
or(equal_points(X1,X2),distinct_points(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t150,plain,
or(equal_points(X1,X2),distinct_points(X1,X2)) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(c48,plain,
( ~ equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))
| ~ convergent_lines(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t56,plain,
or(not(convergent_lines(sk0,sk2)),not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t140,plain,
or(not(convergent_lines(sk0,sk2)),not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(orient,[status(thm)],[t56]) ).
cnf(t585,plain,
true = or(false,convergent_lines(sk0,sk2)),
inference(cp,[status(thm)],[t148,t584]) ).
cnf(t14434,plain,
true = convergent_lines(sk0,sk2),
inference(step,[status(thm)],[t585,t79]) ).
cnf(t595,plain,
convergent_lines(sk0,sk2) = true,
inference(orient,[status(thm)],[t14434]) ).
cnf(t14435,plain,
or(not(true),not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(step,[status(thm)],[t140,t595]) ).
cnf(t14436,plain,
or(false,not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(step,[status(thm)],[t14435,t313]) ).
cnf(t14437,plain,
not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = true,
inference(step,[status(thm)],[t14436,t79]) ).
cnf(t624,plain,
not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = true,
inference(rw,[status(thm)],[t14437]) ).
cnf(t864,plain,
not(equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = true,
inference(orient,[status(thm)],[t624]) ).
cnf(t865,plain,
false = ifeq(true,true,equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),false),
inference(cp,[status(thm)],[t188,t864]) ).
cnf(t14518,plain,
false = equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),
inference(step,[status(thm)],[t865,t77]) ).
cnf(t866,plain,
equal_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = false,
inference(orient,[status(thm)],[t14518]) ).
cnf(t867,plain,
true = or(false,distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(cp,[status(thm)],[t150,t866]) ).
cnf(t14519,plain,
true = distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),
inference(step,[status(thm)],[t867,t79]) ).
cnf(t869,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(orient,[status(thm)],[t14519]) ).
cnf(t13253,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),true),
inference(cp,[status(thm)],[t13251,t869]) ).
cnf(t16435,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t13253,t77]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t41,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t138,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t3,plain,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t155,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t166,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(cp,[status(thm)],[t138,t155]) ).
cnf(t14524,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(step,[status(thm)],[t166,t313]) ).
cnf(t14525,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk1)),
inference(step,[status(thm)],[t14524,t79]) ).
cnf(t898,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk1)) = true,
inference(orient,[status(thm)],[t14525]) ).
cnf(t899,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk1),false),
inference(cp,[status(thm)],[t188,t898]) ).
cnf(t14526,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(step,[status(thm)],[t899,t77]) ).
cnf(t900,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk1) = false,
inference(orient,[status(thm)],[t14526]) ).
cnf(t16436,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t16435,t900]) ).
cnf(t16437,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t16436,t79]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t40,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t139,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t165,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t139,t155]) ).
cnf(t14520,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t165,t313]) ).
cnf(t14521,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t14520,t79]) ).
cnf(t880,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t14521]) ).
cnf(t881,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t188,t880]) ).
cnf(t14522,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t881,t77]) ).
cnf(t882,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t14522]) ).
cnf(t16438,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t16437,t882]) ).
cnf(t16439,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t16438,t79]) ).
cnf(t605,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(cp,[status(thm)],[t139,t595]) ).
cnf(t14443,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t605,t313]) ).
cnf(t14444,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t14443,t79]) ).
cnf(t629,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk0)) = true,
inference(orient,[status(thm)],[t14444]) ).
cnf(t630,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk0),false),
inference(cp,[status(thm)],[t188,t629]) ).
cnf(t14445,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk0),
inference(step,[status(thm)],[t630,t77]) ).
cnf(t631,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk0) = false,
inference(orient,[status(thm)],[t14445]) ).
cnf(t16440,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),sk1),false),
inference(step,[status(thm)],[t16439,t631]) ).
cnf(t16441,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),sk1),
inference(step,[status(thm)],[t16440,t78]) ).
cnf(t13315,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk1) = true,
inference(orient,[status(thm)],[t16441]) ).
cnf(t13316,plain,
true = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk2),true),
inference(cp,[status(thm)],[t1371,t13315]) ).
cnf(t16444,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),sk2),
inference(step,[status(thm)],[t13316,t77]) ).
cnf(t606,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk2))),
inference(cp,[status(thm)],[t138,t595]) ).
cnf(t14447,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk2))),
inference(step,[status(thm)],[t606,t313]) ).
cnf(t14448,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk2)),
inference(step,[status(thm)],[t14447,t79]) ).
cnf(t647,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk2)) = true,
inference(orient,[status(thm)],[t14448]) ).
cnf(t648,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk2),false),
inference(cp,[status(thm)],[t188,t647]) ).
cnf(t14449,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk2),
inference(step,[status(thm)],[t648,t77]) ).
cnf(t649,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk2) = false,
inference(orient,[status(thm)],[t14449]) ).
cnf(t16445,plain,
true = false,
inference(step,[status(thm)],[t16444,t649]) ).
cnf(t13336,plain,
false = true,
inference(orient,[status(thm)],[t16445]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f15_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f16_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f20_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
fof(f21_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c24,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c36,plain,
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f32,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f32_nnf,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c40,plain,
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f33,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f33_nnf,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c42,plain,
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f34,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
fof(f34_nnf,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c44,plain,
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c15,c16,c23,c24,c36,c38,c40,c42,c44,c48]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13336]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.39 % Computer : n005.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Wed Sep 23 11:28:33 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 106.39/14.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.39/14.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------